The generator matrix

 1  0  0  0  1  1  1 3X+2  1 3X+2  1  X  1 2X+2  1 X+2  1  1  0  2 X+2  1  1  1 2X  1 2X+2  1  1 2X+2  1  1 X+2  0  1  1 2X+2  1  X  1 3X X+2  1  1  0  1  X  1  1  1  1  X  1  2  X  1  2  1  1  0  1 X+2  1 2X+2  1 3X  1  X 2X  1  1  1  1  X  1 3X+2  1 X+2  1  1  1
 0  1  0  0 2X  3 3X+1  1 2X+2 2X+2 2X+2  1 3X+3  1 X+1 2X+2 2X  1  1  1  1  1 3X+2 2X+3 3X X+2  1 2X  1 3X+2  2 2X  X 3X X+3  X  2  3  1 3X  1 X+2  3 X+2  1  X  1  2  X  X 3X+1 3X X+1  1  1  1  1 X+1 X+1 2X+2 2X+2 3X+2 3X+2  1  X  1 3X+3 2X  1 3X+2 3X+3 3X+3 3X+3  2 X+2  0 3X+1  1 3X  X 2X
 0  0  1  0  2 2X 2X+2 2X+2  1  1 X+3 X+3  3 X+1 X+1 3X+2  1 2X+3 2X+1  2  2 2X X+3  X  1  0  1 3X+2 3X+3  1 X+2 X+3  1 3X+2  0 3X+1  1  3 3X+1 3X+2 2X+1  1 2X+3 3X+2  2  3 2X+3  X X+3  X  2  1  1 2X+3 X+2 3X+1 3X+2 3X+1 3X  1 2X  1 2X+2 3X+1 3X+2 3X+3 3X+1  1 2X+2 3X+1 2X 2X+1 3X+3  1  0 2X 2X+1 3X X+2 3X+2 2X+2
 0  0  0  1 3X+3 X+3 2X X+1 3X+1 X+3  0 2X+1 3X+2 3X X+3  1 2X+1  0 2X+2 3X+2  1  2 2X+2 X+1 X+2 2X+1  1 2X 3X+1 3X+3 3X+3 2X+3  0  1 3X+3 X+2 3X+1 X+2 3X+3  X 3X+2 3X+1 2X+3 2X  3 2X+2  2 2X+1 3X+3  3 2X+1 3X  2  X X+1 3X+2 X+1  1 3X+2 X+2  1 2X+3 2X+2 3X+1 2X+3 3X+2 2X  1  2 2X+3 X+2 3X+1  2  X X+3  1 2X+3 2X 3X+2  0 X+2

generates a code of length 81 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+542x^74+1556x^75+3275x^76+3912x^77+5902x^78+6080x^79+8498x^80+7064x^81+8260x^82+5772x^83+5650x^84+3688x^85+2634x^86+1176x^87+873x^88+364x^89+162x^90+72x^91+34x^92+8x^93+4x^94+4x^96+4x^97+1x^100

The gray image is a code over GF(2) with n=648, k=16 and d=296.
This code was found by Heurico 1.16 in 52.4 seconds.